It’s true that the rear drum brakes on modern econo-boxes seldom need much work. Most of the stopping action goes on with the front disc brakes, since the car pitches forward when you stop and puts most of the weight on the front wheels. On my Toyota Corolla I have close to 200K miles and had to replace the front pads several times, but never replaced the rear drums or even the rear drum shoes. The shoes are still within their thickness spec.
But that’s my car, a Toyota with a manual transmission. You don’t mention what kind of xmssion you have, but automatics put more wear and tear on the brakes than manuals. And it depends on how your car was driven before you got it. Someone with a lead foot may have owned it. In that case you may well need new rear drums. If so, the price seems reasonable for parts and labor.
The only way to tell for sure is to have another mechanic who has some expertise in brakes, but without a financial interest in the outcome, pull the rear drums and make a determination based upon the measurements and specs. To me, $400 is worth it for a brake job on a car w/150K miles for new rear drums, shoes, and front pads. I’d be inclined to say “go for it”.